Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator

Abstract In this paper, the boundedness of the Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of the p -adic fractional Hausdorff operator on weighted p -adic weak Lebesgue spaces. We also obtain the sufficient condition of commutators of the p -adic fractional Hausdorff operator by taking symbol function from Lipschitz spaces. Moreover, strong type estimates for fractional Hausdorff operator and its commutator on weighted p -adic Lorentz spaces are also acquired.